Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no-go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non-contextual way. In contrast to an earlier theorem [Breuer, Phys. Rev. Lett. 88(2002), 240402] this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy.